The ubiquitin-proteasome pathway plays an important role in regulating cell cycle, neoplastic growth, and metastasis. PS-341 is a dipeptidyl boronic acid inhibitor with high specificity for the proteasome which is being developed to treat human malignancies. The primary objectives are to determine the dose limiting toxcity and MTD of PS-341 when administered as an intravenous bolus twice weekly for one week followed by one week off the drug, in patients with advanced solid tumors and lymphomas. The pharmacodynamics of PS-341 will be evaluated by the measurement of 20S proteasome inhibition in blood. Secondary objectives will be: to obtain preliminary data of changes in p53, p27, E2F and cyclin E in tissue samples; to identify objective tumor response; and to evaluate the relationship between toxicity and 20S proteasome inhibition in blood and accessible tumor tissue.